delicate skin and rashes are all part of the side effects of chemo. Speak with your oncologist and see a dermatologist ASAP to determine what type of rash or rashes you have and what might be causing them. she/he will be able to prescribed creams/lotions and recommend over the counter products. My oncologists have set up two emergency visits for me in the last 3 years. Right now I am on 3 different prescription lotions to treat 3 different skin condition that I did not have until last week. I previously developed Fungal rashes, eczema, among others. I think I have had at least 6 different types of skin conditions caused by treatment since 2009. They come, they go. I see the derm.
You may also have very very dry skin -why not try vanicream it's an over the counter brand that makes products for very sensitive/dry skin and has a super SPF line. You can also get it on Amazon.